AMC8 2000

AMC8 2000 · Q7

AMC8 2000 · Q7. It mainly tests Word problems (algebra).

What is the minimum possible product of three different numbers of the set $\{-8, -6, -4, 0, 3, 5, 7\}$?

集合 $\{-8, -6, -4, 0, 3, 5, 7\}$ 中三个不同数的乘积的最小可能是多少？

(A) -336 -336

(B) -280 -280

(D) -192 -192

(E) 0 0

Answer

Correct choice: (B)

正确答案：（B）

Solution

Answer (B): The only way to get a negative product using three numbers is to multiply one negative number and two positives or three negatives. Only two reasonable choices exist: $(-8)\times(-6)\times(-4)=(-8)\times(24)=-192$ and $(-8)\times5\times7=(-8)\times35=-280$. The latter is smaller.

答案（B）：用三个数得到负积的唯一方法是：一个负数与两个正数相乘，或三个负数相乘。只有两种合理选择：$(-8)\times(-6)\times(-4)=(-8)\times(24)=-192$，以及$(-8)\times5\times7=(-8)\times35=-280$。后者更小。

Topics

AL.017 Word problems (algebra)